IGCSE 2021 Maths 0580/22 May/June

IGCSE 2021 0580/22 May/June (pdf)

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1. The probability that Jane wins a game is 10/7.
   (a) Find the probability that Jane does not win the game.
   (b) Jane plays this game 50 times.
   Find the number of times she is expected to win the game
2. Calculate
3. Emma has 15 mathematics questions to complete.
   The stem-and-leaf diagram shows the time, in minutes, it takes her to complete each question.
4. Write down an expression for the range of k consecutive integers
5. (a) Henrik draws this scatter diagram.
   (b) Each of the four scatter diagrams shows the same set of data.
   A line has been drawn on each diagram.
6. A rhombus has side length 6.5cm.
   The rhombus can be constructed by drawing two triangles.
   Using a ruler and compasses only, construct the rhombus.
   Leave in your construction arcs.
   One diagonal of the rhombus has been drawn for you.
7. (a) Complete these statements.
   The reciprocal of 0.2 is
   A prime number between 90 and 100 is
8. a = b²/(5c)
9. Without using a calculator, work out 2/3 ÷ 1 3/7.
   You must show all your working and give your answer as a fraction in its simplest form

10. (a) Write 0.00654 in standard form.
    (b) The number 1.467 x 10¹⁰² is written as an ordinary number.
    Write down the number of zeros that follow the digit 7.
11. Write 0.04 as a fraction in its simplest form
12. (a) E = {integers greater than 2}
    A = {prime numbers}
    B = {odd numbers}
    C = {square numbers}
    (i) Describe the type of numbers in the set B' ∩ C.
    (ii) Complete the set labels on the Venn diagram
    (b) Shade the region D' ∪ (E ∩ F)'.
13. A, B and C are points on a circle, centre O.
    DA and DC are tangents.
    Angle ADC = 44°.
    Work out the value of x.
14. The diagram shows a trapezium.
    The trapezium has one line of symmetry.
    Work out the area of the trapezium.
15. Complete the table showing information about the congruence of pairs of triangles.
    The first two rows have been completed for you.
    All diagrams are not to scale.
16. A is the point (5, 7) and B is the point (9, -1).
    (a) Find the length AB.
    (b) Find the equation of the line AB
17. Find the gradient of the line that is perpendicular to the line 3y = 4x - 5.
18. f(x) = x² - 25
19. The diagram shows a shape made from an equilateral triangle ABC and a sector of a circle.
    Points B and C lie on the circle, centre A.
    The side length of the equilateral triangle is 12.4cm.
    Work out the perimeter of the shape.
20. Expand and simplify
    (x - 2)(2x + 5)(x + 3)
21. The force of attraction, F Newtons, between two magnets is inversely proportional to the square of the distance, d cm, between the magnets.
    When d = 1 5. , F = 48.
    (a) Find an expression for F in terms of d.
    (b) When the distance between the two magnets is doubled the new force is n times the original force.
    Work out the value of n.
22. Simplify
23. Find all the solutions of 4 3 sin x = for 0° ≤ x ≤ 360°.
24. Solve.

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